A characterization of quasipositive two-bridge knots
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909603600531456 |
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| author | Ozbagci, Burak |
| author_facet | Ozbagci, Burak |
| contents | We prove a simple necessary and sufficient condition for a two-bridge knot K(p,q) to be quasipositive, based on the continued fraction expansion of p/q. As an application, coupled with some classification results in contact and symplectic topology, we give a new proof of the fact that smoothly slice two-bridge knots are non-quasipositive. Another proof of this fact using methods within the scope of knot theory is presented in the Appendix. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_07179 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A characterization of quasipositive two-bridge knots Ozbagci, Burak Geometric Topology Symplectic Geometry We prove a simple necessary and sufficient condition for a two-bridge knot K(p,q) to be quasipositive, based on the continued fraction expansion of p/q. As an application, coupled with some classification results in contact and symplectic topology, we give a new proof of the fact that smoothly slice two-bridge knots are non-quasipositive. Another proof of this fact using methods within the scope of knot theory is presented in the Appendix. |
| title | A characterization of quasipositive two-bridge knots |
| topic | Geometric Topology Symplectic Geometry |
| url | https://arxiv.org/abs/2307.07179 |